Interferometric measurement of non-homogeneous multi-material surfaces

ABSTRACT

Correction factors for the ALR and PTR parameters of magnetic-head sliders are determined by calculating an effective reflectivity and a corresponding PCOR at each pixel of the air-bearing surface. The absolute value of reflectivity at each pixel of the AlTiC air-bearing surface is obtained from an empirical equation relating it to modulation. The ratio of Al 2 O 3  and TiC in the AlTiC surface is then calculated at every pixel assuming a linear relationship between the absolute value of AlTiC reflectivity and the theoretical reflectivity of each constituent. The linear relationship is then also used to calculate the effective (complex) reflectivity for the AlTiC material from the relative concentrations of Al 2 O 3  and TiC at each pixel.

REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of Ser. No. 11/824,127,filed Jun. 29, 2007.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates in general to interferometric techniques forsurface characterization. In particular, it relates to a new approachfor measuring the height profile of a sample having an opticallynon-homogeneous surface resulting from a composite multi-materialstructure.

2. Description of the Related Art

Interferometric profilometry enables the performance of non-contactmeasurements of surfaces with high resolution and at high measurementspeeds. Accordingly, several widely accepted techniques have beendeveloped in the art for calculating surface topography from opticalinterference data recovered from two conventional approaches, namelyphase-shifting interferometry (PSI) and vertical-scanning interferometry(VSI).

Phase-shifting interferometry is based on changing the phase differencebetween two coherent interfering beams using narrow-band light or asingle wavelength, λ, in some known manner, for example by changing theoptical path difference (OPD) either continuously or discretely withtime. Several measurements of light intensity with different OPD values,usually equally spaced, at a pixel of a photodetector can be used todetermine the phase difference between the interfering beams at thepoint on a test surface corresponding to that pixel. Based on suchmeasurements at all pixels with coordinates (x,y), a phase map Φ(x,y) ofthe test surface can be obtained, from which very accurate data aboutthe surface profile may be calculated using well known algorithms.

PSI provides a vertical resolution on the order of better than 1/100 ofa wavelength; thus, it is well suited for characterizing smooth,well-reflecting surfaces. At the same time, the PSI technique has alimited vertical range of application because of the so-called 2πambiguity; i.e., the fact that the phase shift between two beams isrepeated with 2π periods every time the OPD exceeds a distance of λ/2.This “phase wrapping” behavior of PSI leads to ambiguity in themeasurements of the surface profile when the surface features are higherthan λ/2. Thus, in practice, conventional PSI techniques have beenlimited to measurements of fairly smooth and continuous surfaces becauseonly in such cases can phase-unwrapping algorithms be applied toreconstruct the surface shape.

Large-step, rough, or steep-surface measurements, on the other hand,have been traditionally carried out with white-light (orbroadband-light) vertical-scanning interferometry. As conventionallyimplemented, VSI uses a white-light source and the reference arm of theinterferometer is scanned vertically with respect to a stationary testsample (or vice versa). The degree of contrast of fringes produced onthe detector by two interfering beams (instead of their phases) ismeasured as a function of distance between the reference and testsurfaces to obtain information about the test surface. The contrast of aVSI interferogram is maximum when the OPD approaches zero and the testsurface topography may be reconstructed by determining the peak positionof the modulation envelope of the interferogram for each detector pixel.The VSI approach overcomes the limited scanning range associated withPSI techniques, but suffers from significantly lower resolution (about 3nm) and, therefore, is not as precise as PSI.

Together, PSI and VSI make it possible to measure most samples. However,both are based on having a uniform reflectivity at each region of thesample surface corresponding to each detector pixel. (For convenience,the term pixel is used hereinafter to refer both to a detector pixel andto the corresponding region of the sample surface.)

Multi-material structures, hereinafter referred to as “composite”materials or structures, are necessarily characterized by an opticallynon-homogeneous surface because of the different optical properties ofthe materials. In particular, the phase change on reflection (typicallyreferred to as “PCOR” in the art) used for the interferometricmeasurement of a composite structure may vary from point to point on thetest surface depending on the particular composition of the materialilluminated by the test beam. When two or more materials are present ina sample pixel, the resulting PCOR is an undefined combination of thePCORs generated by all materials within that pixel and detected at thecorresponding detector pixel.

Furthermore, composite structures are typically also characterized byirregular surfaces because of the granularity produced by the interfacesbetween materials. This structural characteristic is found to be presenteven when the surface is highly polished. As a result, the single heightproduced by the interferometric measurement at a given pixel isnecessarily incorrect because of the nano-scale non-planar structure ofthe test surface. Therefore, the interferometric surfacecharacterization of test samples made of dissimilar materials has beenproblematic.

The problem is particularly significant with regard to the manufactureof read/write magnetic-head sliders, where precise and rapidprofilometry is essential for quality control purposes. The preciseheight of the various slider components is critical to ensureperformance and long product life. As illustrated schematically in thetop view and cross-section of FIGS. 1(A) and 1(B), respectively,magnetic-head sliders include an air-bearing surface 10 (ABS) made of analuminum-oxide/titanium-carbide composite material (often referred to asAlTiC), a read/write pole-tip region 12, and a trailing edge surface 14made of aluminum oxide. The working distance between the air bearingsurface of the slider and the disk surface affects the potential for amechanical crash as the head flies over the disk. Similarly, thedistance between the pole tip and the disk affects signal loss duringread/write operations.

Therefore, standard tests carried out for quality control duringmanufacture of head sliders involve the measurement of the differencebetween the heights of the ABS surface 10 and the trailing edge surface14 (commonly referred to as the aluminum oxide trailing-edge recession,or ALR, parameter) and of the distance between the heights of the ABSsurface 10 and the pole tip 12 (commonly referred to as the pole tiprecession, or PTR, parameter). The composite ABS surface 10 is precisionpolished in order to render it as flat as possible for optimalfunctionality. Thus, the height of the ABS surface is convenientlyidentified for the purpose of calculating the ALR and PTR parameters byfitting a plane surface 16 to the height data obtained by means of aninterferometric measurement of a predetermined ABS region. However, forthe reasons mentioned above, the composite structure and thecorresponding granularity of the AltiC material tend to produceimprecise height measurements by conventional interferometry.

Various approaches have been used in the art to overcome thisshortcoming of interferometry. For example, one approach has been todetermine global refraction indices (n,k) for the ABS region usingellipsometry and to establishes a linear relationship between n and thereflectance R of the ABS surface. A well-known formula relating PCOR ton and R is then used to calculate a single overall PCOR value for theABS surface, which can be used to correct the inteferometricmeasurement. See K. H. Womack et al., “IEEE Transactions on Magnetics,”Vol. 34, No. 2, March 1998, p. 459.

Another approach is based on the assumption that the effective complexreflectivity, r_(mix), for a mixture of two materials [of composition ε% TiC and (1−ε) % Al₂O₃] is given by the linear relationship r_(mix)=εr_(TiC)+(1−ε)r_(Al2O3). Thus, a theoretical value for r_(mix) is simplycalculated on the basis of known quantities (ε, r_(TiC), and r_(Al2O3)).Global refraction indices (n,k) are then generated by ellipsometry andused in an empirical equation to calculate a global PCOR for the ABSregion as a function of the assumed effective complex reflectivity andthe measured global refraction indices. See Peter de Groot, “AppliedOptics,” Vol. 37, No. 28, October 1998, p. 6654.

Still another approach is disclosed by Mansfield et al. in U.S. PatentPublication No. 2006/0176522. These authors use an empirical formula forcalculating a height correction for the ABS region as a function of theaverage modulation amplitude over the trailing-edge surface, the localmodulation amplitude at the pixel of interest, and several parametersdetermined empirically. Specifically, one parameter is related to theinstrument and is calculated by comparing results obtained from knownsurfaces; another parameter is calculated so as to minimize roughnessfrom a known set of height data; and two more parameters are selectedfor numerical and normalization purposes.

None of these methods achieves the degree of accuracy desired for theinterferometric measurement of ALR and PTR parameters of magnetic-headsliders. For quality-control purposes, it would be very desirable toachieve an accuracy of about 1 nm RMS or better, but current techniquescan do no better than about 3-4 nm RMS. This invention provides afurther advance in the art based on a pixel-by-pixel analysis of thecomposition of the multi-material ABS surface and a calculation of alocal correction factor for each pixel height generated byinterferometry.

BRIEF SUMMARY OF THE INVENTION

The method of the invention is carried out by performing an initialdetermination of the surface profile of a composite material, such asthe ABS surface of a head slider, using a conventional interferometricmethod. The composition of the mixture constituting the compositematerial (Al₂O₃ and TiC, for example) is then calculated at every pixelof the surface using an empirical relation between modulation and theabsolute value of reflectivity and by assuming a linear relationshipbetween the composite reflectivity of a composite material and thetheoretical reflectivity of each constituent.

An absolute value of reflectivity for the composite material is obtainedfrom the empirical relation and the modulation measured while profilingthe sample surface. The concentration of each constituent of thecomposite material is then determined from the absolute value ofreflectivity for the composite material and the theoretical values ofreflectivity of its constituents using the assumed linear relationship.The linear relationship is then also used to calculate an effectivecomposite (complex) reflectivity for the composite material from theconcentration and the theoretical reflectivity of each constituent. Thephase change on reflection, δ_(ij), at each pixel can thus be determinedusing the conventional theoretical relationship between phase change andreflectivity. Once the PCOR is calculated for each pixel, the initialsurface profile is corrected by adding the corresponding fraction ofwavelength to the height of each pixel.

In the more specific case of ALR- and PTR-parameter calculation formagnetic-head sliders, the plane surface fitted to the profile of theABS (AlTic) surface is corrected according to the invention. Therecessions between the ABS surface and the aluminum-oxide trailing edgeand between the ABS surface and the pole tip can thus be refined using acorrected reference plane calculated from actual reflectance data.

Various other advantages of the invention will become clear from itsdescription in the specification that follows and from the novelfeatures particularly pointed out in the appended claims. Therefore, tothe accomplishment of the objectives described above, this inventionconsists of the features hereinafter illustrated in the drawings, fullydescribed in the detailed description of the preferred embodiment, andparticularly pointed out in the claims. However, such drawings anddescription disclose but a few of the various ways in which theinvention may be practiced.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1(A) is a schematic plan-view illustration of a magnetic-headslider include an air-bearing surface made of analuminum-oxide/titanium-carbide composite material, a read/writepole-tip region, and a trailing edge surface made of aluminum oxide.

FIG. 1(B) is a cross-sectional view of the head slider of FIG. 1(A)taken along line B-B in that figure to illustrate the physicalsignificance of the ALR and PTR parameters.

FIG. 2 is schematic representation of an interferometric profilersuitable for practicing the invention.

FIG. 3 is a flow chart of the broad steps involved in carrying out theinvention.

FIG. 4 is a more detailed flow chart of the steps described to carry outthe invention.

FIG. 5 illustrates the efficacy of the correction method of theinvention by comparing the profiles obtained by atomic force microscopy,conventional interferometry, and interferometry corrected according tothe invention.

FIG. 6 illustrates schematically an AlTic structure coated with a DLClayer.

DETAILED DESCRIPTION OF THE INVENTION

The invention lies in the idea of determining an effective reflectivityat each pixel of a composite sample surface and then calculating a PCORvalue for each pixel from its effective reflectivity. As part of theprocess, an empirical equation is formulated to relate the absolutevalue of reflectivity for the composite material to the measuredmodulation produced by an interferometric measurement. The parameterscharacterizing this equation are determined by way of calibration usinginterferometric data produced with two surfaces of known opticalproperties. The composition of the composite material at each pixel isestimated using the local value of absolute reflectivity and assuming alinear relationship between composition and reflectivity. Theconcentration of each constituent is then used to calculate an effectivereflectivity for the composite material at each pixel, from which thecorresponding PCOR value may be obtained.

The invention is described throughout for convenience with regard tocorrecting the ALR and PTR parameters of magnetic-head sliders, but oneskilled in the art would readily recognize that the method can beapplied in the same general way to correct the interferometric profileof any surface that consists of dissimilar materials, with or withoutgranularity, that produce non-uniform optical properties. As usedherein, the terms concentration and composition are used to refer to therelative amounts (or ratios) of the constituent components of thecomposite material. Inasmuch as these concentrations are denoted interms of undefined percentages (i.e., ε %), it is understood that theyare empirical quantities that do not represent a true composition.Accordingly, the fact that these percentages are not expressed in termsof either weight or volume does not impart any ambiguity to the processof the invention.

According to the invention, a conventional interferometric measurementis first carried out to determine phase and corresponding height at eachpixel within some portion of the ABS surface, the trailing edge surface,and the pole-tip region. A conventional interferometric profilometerconnected to an appropriately programmed computer may be used, asillustrated schematically in FIG. 2. As a result of this measurement,experimental height and modulation values, H_(ij) ^(exp) and M_(ij)^(exp), respectively, are available for each pixel of the ABS surfacemade of composite material (namely Al2O3 and TiC). The followingdetailed procedure is then undertaken to correct the experimental phaseand height initially calculated for the ABS surface.

From theory, is it known that the observed experimental modulation ateach pixel is governed by the relationshipM _(ij) ^(exp)=2I ₀ |r _(ref) |°|r _(obj)|−β,  (1)where I₀ is the product of the intensity received by the sample and thereference surface in the areas corresponding to the ij pixel of thedetector; r_(ref) and r_(obj) are the reflectivities of the referenceand object surfaces used for the interferometric measurement,respectively; and β is an empirical parameter that represents modulationlosses in the system. According to one aspect of the invention, Equation1 is written in function only of the absolute value of the reflectivityof the object surface, as follows:M _(ij) ^(exp) =α|r _(obj) ^(th)|−β,  (2)where r_(obj) ^(th) is the theoretical reflectivity of the compositeobject surface, and α and β are system-dependent parameters.

In order to determine the α and β parameters, Equation 2 can be used instraightforward manner in a two-equation system to express theexperimental modulation produced by two materials of known theoreticalreflectivity [such as the Pole Tip (PT) region and the aluminum (Al)region of the slider], as follows:M _(PT) ^(exp) =α|r _(PT) ^(th)|−β,M _(Al) ^(exp) =α|r _(Al) ^(th)|−β.  (3)This system of equations (two equations, two unknowns) can thus besolved analytically to calculate α and β. This approach yields values ofα and β for each pixel of the region of interest, which could be used assuch on a pixel-by-pixel basis to determine correction factors accordingto the invention. However, global average values used for the entireregion have been found to be sufficiently representative to produce goodcorrection results. Therefore, the latter approach is preferred.

Once values for α and β are so determined, a value of compositereflectivity for the composite AlTiC surface, r_(AlTiC) ^(comp), isdetermined at every pixel by solving Equation 2, as follows:|r _(AlTiC) ^(comp)|=(M _(AlTiC) ^(exp)+β)/α.  (4)The composite reflectivity value obtained from Equation 4 is then usedto calculated the composition of the composite material at each pixel byassuming a particular functionality between the composite reflectivityand each of the theoretical reflectivities of the constituents (Al₂O₃and TiC). Based on the proven viability of the linear approach (seeabove, paragraph 12), the assumption that the composite reflectivityresults from a linear contribution of each constituent is preferred,that is,r _(AlTiC) ^(comp) =εr _(TiC) ^(th)+(1−ε)r _(Al2O3) ^(th).  (5)Since the theoretical values of r_(TiC) ^(th) and r_(Al2O3) ^(th) areknown, ε and 1−ε (the concentrations of TiC and Al₂O₃, respectively) canbe calculated using Equation 5.

Because reflectivity is a complex number, the solution of Equation 5 canbe carried out by equating the absolute values of the two sides inquadratic form, that is,|r _(AlTiC) ^(comp)|² =|εr _(TiC) ^(th)+(1−ε)r _(Al2O3) ^(th)|²,  (6)which, from Equation 4, can also be written as|εr _(TiC) ^(th)+(1−ε)r _(Al2O3) ^(th)|²=[(M ^(exp)+β)/α]².  (7)The theoretical value of reflectivity for a given material can becalculated from well-known equations in the art based on each material'sindices of refraction, n and k. Therefore, all variables and parametersof Equation 7 are known except for ε, which can thus be calculated forevery pixel of the ABS surface.

Once the concentrations of TiC and Al₂O₃ (ε and 1−ε, respectively) havebeen determined for each pixel in the region of interest of the ABSsurface, the composition of the composite material is used to calculatean effective composite reflectivity assuming, again, for example, thelinear relationship of Equation 5, i.e.,r _(AlTiC) ^(eff) =εr _(TiC) ^(th)+(1−ε)r _(Al2O3) ^(th).  (8)The phase change on reflection δ for the pixel can then be calculatedfrom the ratio of the imaginary and real components of the theoretical,effective reflectivity so obtained, as represented by the well knownrelationshipδ=arctan [Im(r _(AlTiC) ^(eff))/Re(r _(AlTiC) ^(eff))].  (9)As a result of this process, the PCOR at each pixel of the AlTiC surfaceused to calculate the ALR and PTR parameters becomes available tocorrect the initial AlTiC profile using the conventional relationshipbetween phase and height,H′ _(ij) =H _(ij)+λδ_(ij)/4π,  (10)where i and j denote a particular pixel, λ is the effective wavelengthused for the interferometric measurement, and H′_(ij) is the correctedheight.

Thus, the method of the invention allows the calculation of a correctionfactor for the interferometric profile of a composite surface based onan empirical combination of experimental and theoretical parameters. Thecorrection is carried out on a pixel-by-pixel basis and produces resultsthat reflect the actual physical structure of the composite material.FIG. 3 illustrates in broad descriptive terms the essential stepsrequired to carry out the invention. FIG. 4 is a flow chart of the morespecific steps that can be used to practice the invention, as describedabove.

When used to correct the profile of the ABS surface of conventionalmagnetic-head sliders, the method of the invention, used with someadditional conventional low-pass filtering, has been found torepetitively yield surface measurements with a level of precision in theorder 0.6 nm RMS or better, which is almost an order of magnitude betterthan the results produced by the same interferometric measurement whenno correction according to the invention is implemented. As a result,the ALR and PTR parameters calculated using the method of the inventionare greatly improved. For example, FIG. 5 shows the cross-sectionalprofile (denoted as AFM) of a typical head slider obtained with anatomic force microscope (taken as the true profile and used forreference for comparison purposes), the corresponding profile H obtainedwith conventional profilometry, and the corrected profile H′ produced bythe method of the invention. It is visibly clear that the discrepancy ofthe uncorrected profile with respect to the AFM reference is in theorder of several nanometers. For instance, the average improvement forthe PTR region was about 11.5 nm (from −14 nm to −2.5 averagediscrepancy). In essence, the correction process of the inventionproduced a profile that is substantially true to the AFM profile. Theseresults have been produced with predictable repetitiveness usingdifferent sample materials.

The calculation of the parameters α and β has been illustrated inEquation 3 using modulation and reflectivity data for the pole tipregion and the aluminum trailing edge surface of the slider. This isconvenient in head slider applications because both of these surfacesneed to be profiled in order to calculate the PTR and ALR parametersand, therefore, the modulation data produced by interferometry tomeasure these surfaces are already available and can be usedadvantageously also for the calculation of α and β. However, it isunderstood that any two surfaces can be used for that purpose. Anexternal reference surface that is particularly desirable for itsoptical properties, for example, may be preferred. In such a case, therelevant equations would become,M _(Ref) ^(exp) =α|r _(Ref) ^(th)|−β,M _(Al) ^(exp) =α|r _(Al) ^(th)|−β,  (11)

Magnetic-head sliders are typically coated with a protectivediamond-like carbon layer (referred to as a DLC layer in the art).Therefore, all interferometric measurements discussed above are carriedout through a thin-film of DLC that has to be accounted for in thecalculation of the correction factors of the invention. In particular,the theoretical reflectivities used in the various equations mustconform to the multilayer structures being profiled.

Referring to FIG. 6, for example, the coated AlTiC surface may beillustrated as consisting of distinct Al₂O₃ and TiC regions coated witha DLC layer of thickness L. Accordingly, as one skilled in the art wouldreadily recognize, the reflectivities of the DLC/Al₂O₃ and the DLC/TiClayers can be calculated from the reflectivities of the individual layerconstituents from the relations,

$\begin{matrix}{{r_{{{DLC}/{Al}}\; 203} = \frac{r_{01} + {r_{12}*{\mathbb{e}}^{{- 2}{\mathbb{i}}\frac{2\pi}{\lambda}{({n_{1} - {{\mathbb{i}}\; k_{1}}})}L}}}{1 + {r_{01}*r_{12}*{\mathbb{e}}^{{- 2}{\mathbb{i}}\frac{2\pi}{\lambda}{({n_{1} - {{\mathbb{i}}\; k_{1}}})}L}}}},{and}} & (12) \\{{r_{{DLC}/{TiC}} = \frac{r_{01} + {r_{13}*{\mathbb{e}}^{{- 2}{\mathbb{i}}\frac{2\pi}{\lambda}{({n_{1} - {{\mathbb{i}}\; k_{1}}})}L}}}{1 + {r_{01}*r_{13}*{\mathbb{e}}^{{- 2}{\mathbb{i}}\frac{2\pi}{\lambda}{({n_{1} - {{\mathbb{i}}\; k_{1}}})}L}}}},} & (13)\end{matrix}$respectively, where the indices 0, 1, 2 and 3 refer to air, DLC, Al₂O₃and TiC, respectively, and where

$\begin{matrix}{{r_{01} = \frac{1 - n_{1} + {{\mathbb{i}}\; k_{1}}}{1 + n_{1} - {{\mathbb{i}}\; k_{1}}}},} & (14) \\{{r_{12} = \frac{n_{1} - {{\mathbb{i}}\; k_{1}} - n_{2} + {{\mathbb{i}}\; k_{2}}}{n_{1} - {{\mathbb{i}}\; k_{1}} + n_{2} - {{\mathbb{i}}\; k_{2}}}},{and}} & (15) \\{r_{13} = {\frac{n_{1} - {{\mathbb{i}}\; k_{1}} - n_{3} + {{\mathbb{i}}\; k_{3}}}{n_{1} - {{\mathbb{i}}\; k_{1}} + n_{3} - {{\mathbb{i}}\; k_{3}}}.}} & (16)\end{matrix}$

While the invention has been shown and described herein in what isbelieved to be the most practical and preferred embodiments, it isrecognized that departures can be made therefrom within the scope of theinvention. For example, the determination of ε in Equation 7 could besimplified by neglecting the interference effect, which would lead tothe simpler equation,ε|r _(TiC) ^(th)|²+(1−ε)|r _(Al2O3) ^(th)|²=[(M ^(exp)+β)/α]²,  (17)from which the value of ε can be calculated by solving a single orderequation.

Similarly, rather than using Equation 9 to calculate the PCOR at eachpixel, the complex quantity r_(AlTiC) ^(eff) could be used to find anequivalent n and k for each pixel from the known relation

$\begin{matrix}{r_{AlTiC} = {\frac{1 - n + {{\mathbb{i}}\; k}}{1 + n - {{\mathbb{i}}\; k}}.}} & (18)\end{matrix}$These values of n and k could then be used to determine a δ value ateach pixel (ij) by using the standard formula:

$\begin{matrix}{\delta_{ij} = {{\tan^{- 1}\left\lbrack \frac{2k}{1 - n^{2} - k^{2}} \right\rbrack}.}} & (19)\end{matrix}$

Those skilled in the art will readily recognize that the technique ofthe invention can be used advantageously for various related purposes,such as, for example, determining a local (pixel-by-pixel) effectivereflectivity value for a surface made of a composite material. Thedetailed process outlined below provides such information upon solutionof Equation 8. The procedure could similarly be used to calculate alocal (pixel-by-pixel) concentration of each constituent of the surfaceof the composite material. That information becomes available uponsolution of Equation 7 or Equation 17 above.

In addition, the invention can be used to provide in situ calibration ofthe interferometric profilometer used to practice the invention. Whenthe apparatus is used to measure ALR and PTR parameters, modulation datafor the trailing-edge surface and the pole-tip region are necessarilyproduced and stored. Therefore, these data are available for the direct(i.e., in situ) calculation of the empirical system-dependent parametersα and β required to carry out the step identified with Equation 2.Accordingly, no further calibration of the apparatus is necessary usingreference surfaces and materials that are not already part of the systemand samples being tested.

Note also that the invention has been described using a linearrelationship between composite reflectivity and theoretical reflectivityof constituents (see Equation 5) because such functionality has provento be advantageous for the objective of the invention; however, anyother empirical or theoretical relationship that produces useful resultswould be acceptable to practice the invention following the sameprocedure described herein. Finally, reflectivity is the opticalproperty described for the various steps used to practice invention, butthe approach would be equally viable with any optical property affectingPCOR for which an empirical equation relating it to modulation could bewritten. The same series of steps would lead to the calculation of aneffective value for the optical property, which in turn could be used tocalculate phase change on reflection. For instance, if a material ispartially transmissive, transmissivity and its theoretical relationshipto modulation could be used to define a different empirical equationwith different parameters that could be determined by solving theequation with information from known materials. Thus, in essence, theimportant advance of the invention is the idea of determining aneffective value at each pixel for an optical property that can be usedto calculate the PCOR at that pixel. The details described hereinillustrate only some of the various ways in which the invention can beimplemented.

Therefore, the invention is not to be limited to the details disclosedherein but is to be accorded the full scope of the claims so as toembrace any and all equivalent processes and products.

The invention claimed is:
 1. A method of determining a pixel-by-pixelconstituent composition of a composite material with interferometricprofilometry, said method comprising the following steps carried out ateach of a plurality of pixels of a sample of the composite material:measuring an interference signal produced by the sample of saidcomposite material; assuming an empirical relationship between a knownvalue of an optical property for a material and an interference signalproduced by said material; establishing said empirical relationshipusing interference data produced by materials with known values for saidoptical property; using said empirical relationship to derive a value ofsaid optical property for the composite material; further assuming apredetermined relationship between a concentration of each constituentof the composite material and a contribution of said constituent to theoptical property of the composite material; and calculating saidconcentration of each constituent at each of said pixels using saidpredetermined relationship and said value of the optical property forthe composite material; wherein said measuring step is carried out withan interferometer; and said establishing, using and calculating stepsare carried out with a computer.
 2. The method of claim 1, wherein saidoptical property is reflectivity, said predetermined relationship islinear, and said value of the optical property is an absolute value ofreflectivity.
 3. The method of claim 2, wherein said composite materialis made of an aluminum-oxide/titanium-carbide material.
 4. A method ofdetermining a pixel-by-pixel value of effective reflectivity of acomposite material with interferometric profilometry, said methodcomprising the following steps carried out at each of a plurality ofpixels of a sample of the composite material: measuring an interferencesignal produced by the sample of said composite material; assuming anempirical relationship between a known value of reflectivity for amaterial and an interference signal produced by said material;establishing said empirical relationship using interference dataproduced by materials with known reflectivities; using said empiricalrelationship to derive an absolute value of reflectivity for thecomposite material; further assuming a predetermined relationshipbetween a concentration of each constituent of the composite materialand a contribution of said constituent to the reflectivity of thecomposite material; calculating said concentration of each constituentat each of said plurality of pixels using said predeterminedrelationship and said absolute value of reflectivity for the compositematerial; and deriving said effective value of reflectivity for thecomposite material from said predetermined relationship and saidconcentration of each constituent; wherein said measuring step iscarried out with an interferometer; and said establishing, using,calculating and deriving steps are carried out with a computer.
 5. Themethod of claim 4, wherein said composite material is made of analuminum-oxide/titanium-carbide material, and said predeterminedrelationship is linear.